Cancer is a disease of rare events in single cells, and heterogeneity of cancer cells contributes to disease progression, treatment resistance, and relapse. In recent years, there has been tremendous progress in the development of methodologies to interrogate single cancer cells, including in situ imaging and single-cell DNA and RNA sequencing. Heterogeneity can be both genetic and non-genetic. Genetic heterogeneity - rare mutations in somatic cells which lead to the initiation and pathogenesis of cancer - is well-appreciated. Non-genetic heterogeneity - changes in the phenotype of the cell which may be unrelated to genetic mutations - is only beginning to be understood and is the subject of the investigations carried out in the Systems Biology of Gene Expression section. Although heterogeneity or variability plays an important role in cancer progression, it is also a window into the mechanisms of gene regulation. Thus, even without addressing the role of heterogeneity in a particular phenotype, one can use variations or fluctuations to understand the mechanisms of RNA synthesis and processing in single cells. This principle of using dynamic observations to understand molecular mechanism in living cells is the motivation behind the experiments carried out in the lab. I. Transcription dynamics in living cells: the causes and consequence of expression heterogeneity. One paradigm for genetic control in the metazoan nucleus is steroid receptor-mediated transcription. Steroid receptors coordinate a diverse range of responses in higher eukaryotes and are involved in a wide range of human diseases. Moreover, the ligand-dependent nature of these transcription factors makes them appealing targets for therapeutic intervention, necessitating a quantitative understanding of how receptors control output from target genes. In addition, steroid-response elements often work through long range regulation of genes located megabases away, making them an appealing model for understanding the role of chromosome structure in gene regulation. We are studying estrogen responsive genes in MCF7 cells, starting with the well-studied paradigm of the TFF1 gene and proceeding to large-scale analysis of many genes. We find that even for TFF1, which shows a 60-fold up-regulation upon induction with estradiol, transcription is a rare event, with long periods of inactivity punctuated by short bursts of RNA synthesis. We show this intermittency is the major driver of non-genetic heterogeneity. The key point is that cellular heterogeneity is a dynamic phenomenon and dynamics must be considered at every step, from experiment through to theory and analysis. Moreover, to understand dynamics is to understand mechanism. We approach this problem in three parts using model systems in addition to the estrogen-responsive human system. First, we consider the role of cis-acting regulatory regions in DNA. Next, we ask how trans-acting factors - both protein and RNA - regulate transcription. Finally, we seek to apply these ideas to large-scale experiments in an attempt to bridge the gap between single-molecule biology and genomics. II. RNA processing in normal and transformed cells. Transcription is carried out by a processive enzyme which can be experimentally reconstituted in vitro from minimal components. The spliceosome is different: it is a single-turnover enzyme which assembles and disassembles dynamically on each and every intron. As such, kinetic studies in living cells have much potential for elucidating the mechanism of splicing. We have also shown that RNA processing is stochastic, with single RNAs generated from the same gene in the same cell following different processing trajectories. Thus, RNA processing is another source of non-genetic heterogeneity. In fact, changes in RNA alternative splicing are one of the hallmarks of cancer. Recently, mutations in the general splicing machinery have emerged as important oncogenes in blood malignancies and solid tumors. The mechanism of pathogenesis is unknown. We have characterized one of these mutations in the complex which recognizes the 3' ss of most introns in the human genome (U2AF1 S34F). This mutation slows down splicing, potentially allowing for greater possibilities in alternative splicing. We have continued to work on the mechanism of oncogenesisis for the U2AF1 mutant and identified a phenotype which is a synergistic outcome of noisy gene expression and splicing. Thus, the principles described in this report related directly to disease phenotypes. III. Technology Development. The lab has been at the forefront of single-molecule imaging, analysis, and modeling since its inception in 2011. In particular, two technologies - RNA imaging with phage coat proteins and fluorescence fluctuation analysis -- have been advanced during the last year. We follow single molecules of RNA by inserting a DNA cassette which codes for RNA hairpins. After DNA is transcribed, the RNA is bound through the high-affinity interaction between the RNA and a phage coat protein labeled with a fluorescent protein. These phage coat proteins are either MS2 or PP7. The system is entirely genetically encoded and allows for multi-color labeling of RNA. Although there have been exciting advances in the world of RNA imaging which we are also trying in the lab, those techniques do not yet provide the sensitivity and resolution that we routinely achieve. We analyze this data with correlation functions, which is an approach we pioneered for single-gene analysis. This method is ideal for kinetic studies and provides a wealth of information about transcription and splicing. In this report, we also introduce cross-correlation to understand the relationship between individual alleles. These measurements are carried out on two custom-built single-molecule microscopes which were constructed from 2011-2013. We have also adopted the use of cutting-edge gene editing to label human genes that can then be observed under endogenous regulation. As of this writing, no other laboratory has succeeded in single-molecule imaging of human mRNAs with the same spatial or temporal precision. To achieve endogenous gene imaging, we have had to develop insertion and screening strategies which we expect will be widely adopted by the single-molecule community.